Rule: Q[23, 24]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $\frac{514589420475}{524288}\cdot t^{23}-\frac{2893136075115}{524288}\cdot t^{21}+\frac{7064634602025}{524288}\cdot t^{19}-\frac{9821565178425}{524288}\cdot t^{17}+\frac{4281195077775}{262144}\cdot t^{15}-\frac{2429867476575}{262144}\cdot t^{13}+\frac{902522205585}{262144}\cdot t^{11}-\frac{214886239425}{262144}\cdot t^9+\frac{62386327575}{524288}\cdot t^7-\frac{5019589575}{524288}\cdot t^5+\frac{185910725}{524288}\cdot t^3-\frac{2028117}{524288}\cdot t$
• $P_2$:
  $\frac{514589420475}{524288}\cdot t^{47}-\frac{296140493823135}{25690112}\cdot t^{45}+\frac{1356152536911366675}{21399863296}\cdot t^{43}-\frac{12041134887072399378075}{55575444979712}\cdot t^{41}+\frac{262883710849306779033365475}{509237802349101056}\cdot t^{39}-\frac{431604020951895506619686303925}{474100393987013083136}\cdot t^{37}+\frac{80060286926955923669107273320111285}{64996444176517147149205504}\cdot t^{35}-\frac{4828685181605423813546772459193285358175}{3691213061228585303750529777664}\cdot t^{33}+\frac{18710666120441506756958418066525454313767275}{16911292640018763569133052176367616}\cdot t^{31}-\frac{33018810267978447707203202857673012812036263675}{43918626986128728989038536502026698752}\cdot t^{29}+\frac{314776795259295716242944719626598046844592739529475}{763470611864488186533399433665207042572288}\cdot t^{27}-\frac{504531435605492634928939840368191912247124372079519271}{2762437587044629966295347940325367818721951744}\cdot t^{25}+\frac{6961633920463112685168003705961328458706212260564142826917534425}{106775101289001444451786020321671510606739223081844473856}\cdot t^{23}-\frac{7871588967487446417800903485543617521940513681430132218930825}{422035973474314009690853835263523757338890209809661952}\cdot t^{21}+\frac{255455470192522956699156034394453798473110131903792531192475}{60290853353473429955836262180503393905555744258523136}\cdot t^{19}-\frac{2393811888802884178729589676966722644243007571141733685325}{3173202808077548945044013798973862837134512855711744}\cdot t^{17}+\frac{38592408735431826049532541830061999083460644112842226915}{373317977420888111181648682232219157309942688907264}\cdot t^{15}-\frac{567278794759455532590640777880961437177644174022279025}{53331139631555444454521240318888451044277526986752}\cdot t^{13}+\frac{296546162456637742760110336821678917814537722200646475}{373317977420888111181648682232219157309942688907264}\cdot t^{11}-\frac{107254408309744930189197961589907346636673930663073825}{2613225841946216778271540775625534101169598822350848}\cdot t^9+\frac{3573535994102649827612974667482776099165500472977475}{2613225841946216778271540775625534101169598822350848}\cdot t^7-\frac{9813032072504554486354145372523198489801629561505}{373317977420888111181648682232219157309942688907264}\cdot t^5+\frac{89171449580285733917003341113298637260553528325}{373317977420888111181648682232219157309942688907264}\cdot t^3-\frac{2664533987453158013443795712808313239321250275}{4106497751629769222998135504554410730409369577979904}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Legendre type can be downloaded here packed into a single file.